In this work, we carry out a systematic study of the dissipative AB chain, focusing on its topology and detection. We identify an additional topological phase transition beyond the experimentally demonstrated parameter regime, and derive analytical expressions for the topological transition points using the non-Bloch band theory.
Invoking the theoretical framework of Feshbach projection [1]}, [2]}, we derive the transfer rates of the experimentally implemented atom-injection spectroscopy, which are in good agreement with numerical simulations. In the experiment, atoms were injected to an open edge of the AB chain, to detect the topological edge states. Here we show that by injecting atoms into a bulk site far away from the boundary, spectral information under the periodic boundary condition can be obtained from the transfer rate.
We then propose a dynamic detection scheme for the topological edge states.
